Question

what is the formula for the derivative of
a^x
a^u

Answer 1

can you tell which of them are constants and derivative wrt to which variable

Answer 2

assuming that both x and u are variables, x is a variable and u is constant?

Answer 3

if they were both variables, the use the D-operator, or implicit diff eq. method in both cases otherwise one of them you use the D-operator and the other one would be zero if and only if u is a constant

Answer 4

Please ask the right and complete question in order to not confuse yourself and get the right answer as accurate as possible

Answer 5

\[y = a ^x \]

Answer 6

Step one: take the natural log of both sides

Answer 7

\[lny=lna^x \rightarrow lny=xlna\]

Answer 8

step two: differentiate both sides

Answer 9

\[\frac{ dy }{ dx }\frac{ 1 }{ y }=lna \rightarrow \frac{ dy }{dx }=ylna\]

Answer 10

step three we know that \[y =a^x, hence \frac{ dy }{ dx }=a^xlna\]

Answer 11

that is the complete answer, if u is a constant then you will get a zero when you differentiate a^u assuming both a and u are constant, however if u is not a constant but a variable then use the same method we applied for a^x, but what is a is a variable and u is a constant then you use the famous ua^u-1.